For many practitioners and market participants, the valuation of financialderivatives is considered of very high importance as its uses range from arisk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods...

Understanding the behaviour of the American put option is one of the classic problems in mathematical finance. Considerable efforts have been made to understand the asymptotic expansion of the optimal early exercise boundary for small time near expiry. Here we focus on the large-time expansion...

This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number...

Droplets on insulators in outdoor high-voltage equipment move and leave water films on the insulating material. These films further the development of undesirable electric currents or even flash-overs. The paper deals with the behaviour of a single droplet laying on a solid support in a strong...

We present three approaches to value American continuous-installment options written on assets without dividends or with continuous dividend yield. In an American continuous-installment option, the premium is paid continuously instead of up-front. At or before maturity, the holder may terminate...

Outdoor high-voltage equipment is exposed to rain and moisture. Water droplets on the surface of insulators influence negatively the insulating and hydrophobic material properties. The shape of the droplets signifies the state of the aging material. The present paper develops a numerical...